Abstract Quadratic curve and surface fitting to a set of data points are fundamental problems in reverse engineering and many other application areas. We develop the fitting methods for quadratic curves and surfaces based on the squared distance minimization technology. The basic idea of squared distance minimization for curve and surface fitting is first presented. Then we devise the corresponding squared distance term for each quadratic curve and surface, and minimize it to obtain its parameters. We repeat the squared distance minimization and update the parameters of the quadratic curve and surface by iterations until convergency. Consequently, the final fitting result is achieved. Experimental results demonstrate the effectiveness of the fitting method.